(CD7) Weighted AUC (t)

Lambert and Chevret [5] used a similar approach to Heagerty and Zheng [12] and proposed a time-dependent weighted AUC estimator restricted to a fixed time interval (τ ₁, τ ₂) and defined as:

where t ⁽ⁱ⁾ are the ordered distinct failure times for which, if t ⁽¹⁾ > τ ₁, it is assumed that t ⁽⁰⁾ = τ ₁, Ŝ(t), is the Kaplan-Meier estimate of the survival function and AUC^C,Dt is a nonparametric estimator of a C/D time-dependent AUC such as CD2or CD5 or any other estimator. The value τ ₂ can be allocated as the value slightly below the maximum expected follow-up time if no clinically motivated choice is specified [22]. Bootstrap resampling is used to compute the confidence intervals of CD7. Since this weighted AUC is defined under C/D, it is not directly related to concordance measures, unlike the integrated AUC that will discuss under I/D definition. However, the proposed estimator is better understood by physicians and also closer to the clinical setting since most clinical studies want to distinguish between individuals who fail and individuals who survive the disease from baseline to any particular time t. It is easy to implement since it can use any C/D estimators.